Finding the Distance Revamped!

"Finding the Distance" foldable was requested in the form of a pdf.

Finding the Distance

I have typed it up and uploaded it as a word document (editable) and as a pdf. An answer key has been uploaded also. As always, printing can be tricky. I print "two sided along the short edge". After printed, you'll notice a dotted line along one short edge. Cut along the dotted line so that the foldable will fold up nicely.

First unfold reveals methods for distance off a slanted line along with using method 1. 

Second unfold reveals the use of method 2. 

The order of the methods did not hold a significance initially. I now teach the use of the Pythagorean Theorem first to bridge a connection the the distance formula.

Fundamental 5

Fundamental 5

This is a training that we did the week before school started. I was very resistent initially until some of the ideas fit into my style of teaching. I am giving it a shot!

The idea is that if you teach all five of the strategies in unison, then the lesson will be more effective and benefial for the student. It makes sense and I fill that I have some down already.

Fundamental 5:

1. Frame the Lesson - State the objective using the language of the standards, if possible; and then state the finishing product or task completed by the students. (I need to work on this.)

2. Power Zone - Teaching and working in and around the kids. (I feel like I'm an ace here. I am always in their business and constantly grading their work as we go.)

3. Frequent and Purposeful Talking - (I am working on this. I am still uncertain of it's meaning.)

4. Recognize and Reinforce - This is where a teacher recognizes and reinforces the positive behaviour with specifics. (I am very good here, but need to work on identifying the specifics-saying student's name and the behaviour.)

5. Writing Critically - (This is where I yearn to grow the most. I have been looking for strategies in this area for two years now. I finally have some answers. This is also one of my two weakest areas.)

So, how did this click into my style of teaching? Well, I already feel pretty confident in working the power zone and recognizing and reinforcing the behaviour I want to see. We talk a lot in my class about the math and create as much cross curriculur relevance as we can. The two areas that I really wanted to improve on and have for several years now is writing objectives and writing critically with kiddos. I think writing is extremely important and can make a huge difference in a student's education. And not just writing by hand, but anything that involves the proper language students should know and use. I think that writing 'critically' is the bridge from basic low level thinking to that high level thinking that is required of kids on standardized tests.

Writing scares me! It takes more forever to write an email, letter of recommendation, or even a post it note to another teacher. Don't even get me started on the scary mess that was my college english experience! I think the only place I can comfortably write is in the math journals and maybe my blog. I still read a blog entry three to four times before I post (hence, why it takes me forever to get anything out!).

So, why do I think I have found a fit in this fundamental five? Well the left side of our journals have always held a special place in the back of mind for some kind of writing, and I think I might have an idea.

We start each page with our objective or frame of the lesson on the top left page. I really try to focus on sentence structure and the verbs I use. I want kids to be able to describe what they are doing and how they are doing it using the higher levels of bloom's taxonomy.

Critical writing?

This has been the harder piece of the puzzle to fit in. I googled 'critical writing stems' and ran across some great writing stems for all subjects that are broken down into the bloom's taxonomy categories. Sometimes the question is written when we begin the lesson, and other times, the question develops throughout the lesson. I just go with the flow. For example, I couldn't think of a critical writing question for the Sets of Real Numbers lesson and thought that I would wait and see. Sure enough, while we were discussing sets and subsets, the students didn't like my ideas of relevance (classifying things using kingdom, phyllum, class, etc.) and they started coming up with their own! The next day, as a starter, I had students write or illustrate their own idea of sets and subsets. The results were random and unique to each student; it was great!!

 

Overall, writing the lesson objective (framework) and writing critically is a work in progress. I am able to do this much more consistently this year because I have a place to put it and the students are expecting it. We'll see how it goes.

 

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My First Week of School... slower than expected

I had my first several weeks of notes and assignments all planned out. I guess I thought it could be taught in one week.

It did not go as planned! (It never does.)

I used the "First Day of School" tangram for all my classes. It was a great way to determine the pace at which a class or student cuts, folds, and pastes things together. The pace of my previously taught classes is significantly more efficient than that of my new students.

The great thing about doing the reference chart on day one is that my students immediately use it without being reminded to. In Pre-Algebra, we began the year with a review of Geometry Formulas. I was concerned at first, but realized that this was a great review of basic algebra skills with something they were familiar with. And it was another way to bridge the arithmetic skills from by hand to calculator.

Every class then created a Unit Pocket for the first unit.

In Algebra 2, we started with Sets of Real Numbers. I reference the textbook partly for my information and loved the example they used-billiard balls.

For the sets and subsets of rational numbers I printed a concentric rectangles to give the look and feel of a Venn diagram. My original strategy was to teach rational numbers first and work towards natural, but my colleague suggested and explained how she teaches natural numbers first and works out towards rational. It made complete sense and it worked my kids!!

For Geometry, I have followed the original pages from older posts, but decided to add this page to clarify what happens to triangles in the different types of geometry.

This year for Taxi Cab geometry, I used google earth to show students where it originated-New York. For small town kids, this was an adventure. We then used google earth to find our small town, overlayed a sheet of posterboard on the Promethean, and tried to find the shortest route from school to the Snow Cone truck. Taxi Cab geometry was just about everyone's favorite.

 

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Course Syllabus

I have written a course syllabus for geometry and math models in the past. However, when I turned in my school laptop and transferred schools, those course syllabi seem to be the only documents that I did not transfer. I have rewritten my course syllabus and am looking for some feedback. This might also give some insight into the 'method of my madness.'

Writing has always been a tough area for me. Writing even an email takes me up to 30 minutes. It can take me days to complete a blog post. Whenever I have to write a letter or something, I tend to look for a template or similar document for guiding structure and format.

Some of the information in my course syllabus is pulled and adapted from websites such as TEKS (Texas teaching standards) and academic integrity. I really like the wording of these sights and couldn't come up with a better way. I tried my best to document so that I do not plagiarize. Definitely lend support and advice here.

Please post feedback. Am I missing something critical? Could something be better written?

The syllabus given to each student will be course specific.

 

Course Syllabi: Algebra 1, Geometry, Algebra 2

Course Description:

The course of Algebra 1 relies on the prior knowledge presented in K-8. A student is expected to have a basic understanding of number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry; measurement; and probability and statistics prior to this course. Throughout this course a student is expected to use algebraic thinking and symbolic reasoning; represent and model functions in order to analyze and interpret relationships; use a variety of methods to set up and solve equations and inequalities in relation to functional relationships; use a variety of representations, tools, and technology to model mathematical situations to solve meaningful problems; and implement the underlying mathematical processes. (Description is an adaptation and summarization of the TEKS for Algebra 1.)

Course Description:

The course of Geometry relies on the prior knowledge presented in K-8. A student is expected to have a basic understanding of number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry; measurement; and probability and statistics. A student is expected to acquire geometric thinking and spatial reasoning; knowledge of geometric figures and their properties; understand the relationship between geometry, other mathematics, and other disciplines; use and apply tools for geometric thinking; and implement the underlying mathematical processes. (Description is an adaptation and summarization of the TEKS for Geometry.)

 

Course Description:

The course of Algebra 2 relies on the prior knowledge presented in K-8. A student is expected to have a basic understanding of number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry; measurement; and probability and statistics. Throughout the course of Algebra 2, a student is expected to use algebraic thinking and symbolic reasoning to study algebraic concepts and relationships; analyze and understand the relationship between functions and equations; perceive connections between algebra and geometry; use a variety of representations, tools, and technology to model mathematical situations; and implement underlying mathematical processes.

(Description is an adaptation and summarization of the TEKS for Algebra 2.)

Contact Info:

Tiffany Haley thaley@baird.esc14.net Rm: 24

• Reminder 101 - Algebra 1 text @eab1 to (325) 480-3682 (I plan to use reminder 101 to inform students of events and major grades such as exams and journal grades.)
• Reminder 101 - Geometry text @b288d to (325) 480-3682 (I plan to use reminder 101 to inform students of events and major grades such as exams and journal grades.)
• Reminder 101 - Algebra 2 text @81a64 to (325) 480-3682 (I plan to use reminder 101 to inform students of events and major grades such as exams and journal grades.)

Classroom Hours:

Tutorials: 7:30 am to 8:00 am

1st Period: TBA

2nd Period: TBA

3rd Period: TBA

4th Period: TBA

5th Period: TBA

Lunch: TBA

6th Period: TBA

7th Period: TBA

8th Period: TBA

Tutorials: 3:35 pm to 4:00 pm

 

Classroom Expectations:

The student is expected to:

• be prepared for class by having the appropriate supplies.
• be on time.
• be dismissed when the teacher dismisses class not the bell.
• be respectful and supportive of others. Mrs. Haley's classroom is a safe environment for you to learn and explore the world of mathematics. This is a NO BULLYING ZONE!.
• clean up after oneself and put up classroom supplies.
• do the best that he or she can to become an independent lifetime learner.
• and, above all, adhere and follow the student code of conduct.

 

Academic Integrity:

A student is expected to follow the Code of Academic Integrity. Academic integrity requires a commitment of five fundamental values: honesty, trust, fairness, respect, and responsibility. The following behaviors violate the principles of academic integrity and are thus prohibited. These behaviors include: plagiarism; cheating; duplication of submission of the same work; collusion; false information and lying; falsifying academic documentation and forgery; theft, abuse, and destruction of academic property; unauthorized use of information technologies; and aiding and abetting academic dishonesty. Ignorance of the Code is not a valid reason for committing an act of academic dishonesty. (Adapted from the Statement of Academic Integrity of Canisius College.)

 

Honor Pledge:

I pledge to maintain a high level of respect and integrity as a student representing Baird High School. I understand and will uphold the Honor Code in letter and spirit to help our school advance authentic learning. I will not lie, cheat, plagiarize or be complicit with those who do. I will encourage fellow students who commit honor offenses to acknowledge such offenses to their teacher or the Honor Council. I make this pledge in the spirit of honor and trust. (Adapted from the International Center for Academic Integrity.)

 

Bathroom Pass Policy:

Two bathroom passes will be provided at the beginning of each six weeks. Here are the multiple purposes of a bathroom pass. (On occasion additional bathroom passes may be awarded.)

1.With permission of the teacher, a student may use a bathroom pass to exit class to go to the restroom, get a drink, go to the office, or go to a locker. When a student chooses to use a bathroom pass and miss the notes, the student is responsible for making notes up on their own time. The lesson will not stop to allow a student to catch up.

2. At the end of each six weeks, a bathroom pass has a value of 5 points that will be added first to the six weeks exam then to the lowest major grade. A maximum of two bathroom passes may be used for bonus points on major grades.

 

Supplies:

There are two supplies required for my classroom. These supplies need to be ready and with the student when attending class on day one. Supplies will be available for purchase before class.

1. Composition Book (not spiral) (Available for $1)

2. No.2 Pencil (Available for $0.25)

**Optional supplies needed for the classroom this year are dry erase markers. A bathroom pass will be given in exchange for a donation of dry erase markers.

 

Journal Policy:

• Composition Book must be used.
• All pages must remain in your journal; do not tear them out. (I plan to use all pages.)
• If notes are missed due to an absence, then the student is to attend tutorials the following day to make them up. Notes are not to be made up during class time while a new lesson is being taught.

 

"Must Have a Pencil" Policy:

A student must have a pencil for class. If a pen is needed, it will be provided by the teacher.

If a student does not have a pencil, then here are a student's options.

1. Borrow from a classmate.

2. Bargain with a bathroom pass.

3. Purchase one for $0.25.

4. Detention!

 

Attendance Policy:

• A student must attend a minimum of 78 days in the fall and 82 days in the spring. Excused, unexcused, medical, and religious absents count against the students attendance.
• If a student is absent, then the student is expected to attend tutorials the following day.
• If a student is not in their seat when the bell rings, then the student is tardy. Three tardies accumulate to an absence.
• If a student is absent from class for more then fifteen minutes, then the student is considered absent for that period.

 

Extracurricular Activities:

• Participation in extracurricular activities is a privilege, not a right (Student Handbook).
• When an absence due to extracurriculars occurs, the students is expected to attend tutorials the following day to make up notes, assignments, quizzes, etc.

 

Grading Policy:

• Grade reports are provided at the beginning of each week.
• If there are missing assignments from the previous week, then a student has until the end of the current week to turn it in before it will no longer be available or accepted.
• These assignments, turned in a week later, are considered late and the resulting grade will be reduced by 10%.
• For the last week of the six weeks, assignments and late work from the previous week and current week are due by the end of day Thursday.

Major Grades60%

Quizzes 25%

Daily Work 15%

 

Course Outline:

First Day of School: 08/26/2013

1st Six Wks Exam: 10/02/2013

Grades Due:10/03/2013

Fall Midterm: 10/16/2013

2nd Six Wks Exam:11/13/2013

Grades Due: 11/14/2013

Fall Semester Finals:12/16/2013 - 12/20/2013

3rd Six Wks Exam: 01/08/2014

Grades Due: 01/09/2014

4th Six Wks Exam: 02/19/2014

Grades Due: 02/20/2014

Spring Midterm: 03/19/2014

5th Six Wks Exam:04/09/2014

Grades Due: 04/10/2014

6th Six Wks Exam: 05/21/2014

Grades Due: 05/22/2014

Spring Semester Finals: 05/27/2014 - 05/30/2013

 

Course syllabus is subject to change. Adequate notification will be provided.

REVISED: 8/10/2013

 

Please detach and return the signed portion.

-------------------------------------------------------------------------------------------------------

 

I have carefully read and hereby agree to the conditions set forth in the course syllabus.

 

Student Signature: ___________________________________Date: __________

 

Parent/Guardian Signature: ____________________________Date: __________

 

 

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Method to my madness!! Building Journal Pages:

Questions: How do you create a journal page or foldable? Where do you start? How do you come up with it?

I'm not sure if I've written about this yet, but it is definitely on my mind quite a bit. My second year co-teacher always asked, "How do you come up with this?"

The answer to that question has been on my mind all through my third year of teaching. So let me see if I can lay it all out.

Step 1: I start with a general objective, select an assignment, and check to see that it aligns with the quiz and unit assessment.

This strategy evolved from the curriculum director at my previous school. "Keep the end in mind." When planning you want to continually loop through and keep the assignment, quiz, and assessment in mind as you plan a journal page, lesson, activity, etc.

I have several EOC prep books that I use for quizzes and the CSCOPE curriculum for unit assessments. I always start by taking the quiz or assessment myself. I work each problem in as many different ways as I can and note each strategy used. The hardest strategy for me to see is always the logical approach. Usually, this method comes out during the lessons from my students. I know that this idea looks and feels like teaching towards a test, and it probably is, but I do what I can.

Step 2: Now that I know what we're working towards, I take the concept, topic, or objective and begin my research. I look online mostly, reference CSCOPE curriculum, Glencoe textbooks, EOC prep guides, colleagues, etc. I try to reference a minimum of four to make sure I have confirmed my findings.

Step 3: Time to organize. I look at the information that I want to convey to my students and begin to think about the method that would best fit this lesson.

• Are we defining something?
• Is this too much at one time?
• Do I need to break this into mini lessons with guided and independent practice loops? (That's what I did for special right triangles this past year and it worked out great.)
• What will this journal page or foldable contain?
• Will it define and organize the concept, contain a reusable manipulative, be the result of a paper folding activity or lesson, a reference of guided practice, or all of the above?
• What is the point of this journal page and how will it benefit my students?

Once I decide the purpose, I then begin to look for or create a foldable that will organize the information and lesson into sections.This is important to me. I like information to be organized, sectionalized, bolded, boxed, highlighted, etc. Kids tend to remember things like that. A lot of times, we'll end up with glued attachments here and there to accomodate new information or make a little more room.

I can't really explain how I come up with my lesson. I've been told that my wacky brain is hard to follow. Sometimes, the lessons are from colleagues, workshops, or previous experiences that I tweak to fit my agenda. My goal on each journal page is to take an overload of information, organize it, and make it relatable to my students. If you've read previous posts, you'll see where I ask for suggestions on how to make a journal page better.

I'll admit, I am not always this on top of my lessons. Sometimes, I walk in knowing what I need to teach, but not how. My go to "don't know where to start" strategy is to go with a blank white sheet of paper. My students know to use my go to short fold half page foldabable. It's boring but I can expand this, glue attachments, glue it like a pocket for additional stuff, and initially this simple foldable provides three sections for attempting to organize. I use this foldable alot, even if we're not writing much. I don't want to run out of room. (Occasionally, I come up with nothing. I turn to a printed paper lesson. We glue together like a book and then into our journals.)

During the past year, my geometry class actually wrote on a lined page in the journal.... twice maybe. There's never enough room and I like to contain a concept to one page. We actually used 90 of the 100 sheets in the composition book. I did only use the front side, but hope to use the back/opposing side as a reflection, sentence stem, summarizing, something page.

Step 4: Once I know how I want to organize and relate, I create a quick disposable mock up of what I plan the journal page to look like. I scribble an outline and notes to self. This is usually something that I use as a guide to keep me on track and throw away later.

Step 5: (optional) Sometimes, I create a pre fab printable foldable template. This makes journaling go much faster and students are less likely to fall behind or make mistakes. I usually have one foldable completed to show students what we're trying to make. Some students are quick to figure it out and begin to help others. I use solid lines to indicate folds and dotted lines to indicate 'cut here'. This strategy can save time by having the students write less and provides structure to help them better organize the information. However, I am a huge advocate of students writing! I think my students have learned more this past year than the previous two because they wrote everything. I rarely printed definitions, diagrams, illustrations, proofs, etc. It was sometimes hard, but my students were better off. Watching them draw platonic solids and cross sections was entertaining, but extremely difficult. I did give in in the end and printed them off. However, anytime I print something off, I still require students to participate by highlighting, fill in the blank, notating, etc.

Step 6: I teach the lesson. I try to make every step of the process engaging and mathematical. I ask open ended guiding questions before, during, and after the creation of the journal page. (I have developed excellent wait time. It was hard, but I'm quite proud of that.)

Even the foldable itself is a mini math lesson. I try to use mathematical language when referencing folds. It took about half a year to come up with new terms for hot dog and hamburger fold. Actually, a student suggested long or short half fold and I've used it ever since.

One time in geometry, I needed the students to fold a blank piece of paper to get sixteen boxes. They recognized a pattern in the words I was using - one half, one fourth, one eighth, one sixteenth. It turned into a mini lesson on exponential functions.

Is this strategy full proof? Absolutely not! I usually change a journal page up year to year, class period to class period. My students are my guiding force, and they let me know what works. Someone once told me that you have to learn to teach students and not just teach a curriculum.

 

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Geometry: Non-Central Angles, Interior and Exterior Angles, and Secant and Tangent Relationships of Circles

Pg 5. Non-Central Angles (Need to rethink the title now that I think about it.)

This page consists of a half page fold of two pages glued together with four half page folds on each page. This entire page is pulled from the CSCOPE curriculum and tweaked just a bit.

First, we completed a page/lesson using paper folding and making conclusion based on what we know. When complete, the students would make a conclusion based on the evidence. We wrote that on the front off that page. After we completed all four pages, we went to the front and wrote three summarizing conclusions. I think it went pretty well and soundly build and understanding.

First section:

Left side:

I drew up a general diagram for the following three pages. We then completed the lesson with the same diagrams.

Right side:

Second Section:

Left side:

Right side:

 

Pg 6. Circles, Lines, and Angles

I want to find a better way to present and organize the following two pages. My students understood, but it didn't make a lasting impact.

 

 

 

Pg 7. Secant and Tangent Relationships

 

 

 

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Geometry: Polygons and Angles in Regular Polygons,

I heavily relied on the CSCOPE curriculum, End of Course prep book, and online resources to guide me through this unit. This is my first year to get this far journal wise and thoroughly teach properties of two dimensional figures.

Pg 1. Unit 7 Properties of Two Dimensional Figures

When I get the whole Youtube thing figured out, I will try and share some paper-folding lessons I've learned in workshops and used in my classroom. They strongly support the unit on two dimensional figures and they are fun!!

Pg 2. Polygons

This is an unusual foldable, but I love how it organizes the concepts I'm trying to get over to my students. It's folded into fourths. The right side is folded two times into itself and the the left flap folds over top to the right. (Sorry if this explanation is terribly confusing; hopefully the pictures make more since.)

Again, there's some gray area as far as complex polygons go, and I informed my students as such. Any opinions or suggested resources, please share.

Next year, I plan to use color to compare corresponding categories.

Complex vs Simple

Concave vs Convex

Irregular vs Regular

Pg 3. Angles in Regular Polygons

I enjoy teaching this lesson because students need multiple ways to determine angles and experience deriving the formulas from building patterns.

We started with a large polygon on the front and illustrated what is considered the interior and exterior angle. Next, I asked them to make a conclusion based on what they know. They concluded that the interior and exterior angles are supplementary! We added that statement to the top. We then went to the inside and completed the gigantic table to derive the formulas. We finished by writing the important formulas and ideas on the front inside the large polygon.

Students struggled with remembering the formula for the measure of an interior angle. They found another way - determine the measure of an exterior angle (easy), and subtract the measure of exterior angle from 180 to determine the measure of the interior angle. A much longer process (to me), but I was so excited that they could figured an interior angle measure out based on concrete prior knowledge.

 

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Venn Diagrams: Quadrilaterals and other Polygons

These activities are AWESOME! I love the discussions that come up, the type of thinking that occurs, and the multiple possibilities there are.

These materials were provided through a workshop. I have yet to use them in my classroom, but I have no doubt these would be an excellent addition to the unit of quadrilaterals.

You start with four different Venn Diagrams.

 

 

 

You have a selection of set titles and shapes.

Here are some examples of the use of these materials.

(Don't forget about the universal set on the outside of the circles.)

 

 

Some suggested strategies/conversations:

• Have a student demonstrate their Venn Diagram.
• Have students justify their decisions.
• Start with with set titles and categorize shapes.
• Start with categorized shapes and determine the set title.
• Ask students where they started and how they categorized the shapes.

 

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Quadrilaterals Project From My Second Year

My secret.... Sometimes when I'm not sure where to start, I go to my students. My second year of teaching, I got to the unit of quadrilaterals and had no idea where to start. I decided to assign an exploratory based project to my honors class and see what turns up.

Objective: Students design and create a graphic organizer on the topic of quadrilaterals.

It began as a very open project and resulted in some unique results. I gave them several days to research, design, and produce their graphic organizer. We used a round robin strategy to evaluate and rate the graphic organizers on display. After this, the students were to choose a graphic organizer and complete one of their own for their journal containing the generalized information of the class.

 

The following are student products and may contain copyright violations and incorrect information.

1. Multi Shutter Fold within Large Shutter Fold

This was by far the most creative and the inspiration for the Properties of Quadrilaterals foldable I now use.

2. Basic Half Page Book Fold

3. Shutter Fold

4. Shutter Fold

5. Half Page Book with Post-it pop ups

This student is one that always makes me smile-unique, challenging, and brilliant. His graphic organizer turned into "what is not a quadrilateral" and I think he enjoyed exploring other shapes more. He used post-its to summarize/justify why the shape is not a quadrilateral.

6. Attribute Pop-up

This graphic organizer is great!! They drew individual quadrilaterals and added pop-ups for definitions. Not overly organized, but I still like it.

7. Trifold Computer Generated

8. Half Page Book

I don't know how I feel about the quadrilateral web, because it depicts a parallelogram as being a subcategory of a trapezoid. That was another gray area topic. It was a good conversation to listen to when the kids evaluated this graphic organizer.

9. Half Page Book

10. Layered Flip Book

 

I collected the above graphic organizers, combined some styles that I liked, and produced the following graphic organizer that I used this past year. I am always still working on facts and information. So if you have any critiques or suggestions, please comment.

 

 

 

The second half of the project consisted of an essay.

Options:

• Write two full pages analyzing the attributes and relationships of quadrilaterals.
• Depict the attributes and relationships of quadrilaterals using fiction.

I ended up with quite a bit of plagiarism which was a violation of the course syllabus and resulted in failing grades and reprimands.

However, the best result is the relationship a student told of a rectangle and a rhombus. "Rectangle and Rhombus stayed out late one night, and nine months later they had Square."

 

EXTRA: This is my first quadrilateral foldable experience from a journaling workshop.

 

 

 

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